Question

If a man's face is 25 cm in front of a concave shaving mirror producing erect image of 1.5 times the size of face, focal length of the mirror should be:

• A. 75 cm
• B. 25 cm
• C. -75 cm
• D. 60 cm

Hint:

Using the formula \(m = \frac{f}{f - u}\) directly saves time during exams by avoiding the need to calculate the image distance \(v\) first.
Be extremely careful with sign conventions for \(u\) and \(m\).

Answer 1

The Correct Option is C

Step 1: Write down what is given.
The face is $25\text{ cm}$ in front of the mirror, so $u = -25\text{ cm}$, and the image is erect and $1.5$ times bigger, so $m = +1.5$.
Step 2: Use the image distance form of magnification instead.
For mirrors, $m = -\dfrac{v}{u}$, so we can find $v$ directly: \[ v = -m u = -(1.5)(-25) = 37.5\text{ cm} \]
Step 3: Feed this value of $v$ into the mirror formula.
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{37.5} + \frac{1}{-25} = \frac{2}{75} - \frac{3}{75} = -\frac{1}{75} \] So $f = -75\text{ cm}$.
Step 4: Confirm the answer.
The negative sign is expected since a shaving mirror that magnifies an object held close to it is concave, and the number matches what we need.
\[ \boxed{f = -75\text{ cm}} \]